Calculus I Review
Keep
in mind that you should understand key concepts in a variety of ways:
- graphically (draw a picture
which explains it)
- algebraically (write a
formula for it)
- numerically (compute a value
for it)
- in words (write a description
of it)
Chapter 1 - Library of
Functions
- Functions (definition,
examples, expressing functions as formulas, as tables, as pictures, and in
words)
- Domain, range
- For each of type of function:
What is the basic shape of the graph? What is the general form of the equation?
How can you determine an equation, given a graph? given a table of data?
What are the important characteristics of each function? Are these
functions invertible? In what types of applications will you
encounter these functions?
- Linear functions
- Exponential functions
- Logarithmic functions
- Trigonometric
functions and inverse trigonometric functions
- Power functions,
Polynomial functions
- Rational functions
- Inverse functions (find
inverse functions algebraically, graphically, numerically, and describe
inverse functions in words)
- Composition of functions
(including transformations such as shifting, stretching, reflecting), sums
of functions
- Modeling various sorts of
functions (checking differences and ratios in y-values when differences in
x-values are constant, using log plots, finding trig functions with
particular properties)
- Continuity
Chapter 2 – Limits, Average and
Instantaneous Speed
- Limits
- Average
speed on an interval [a,b]
- Instantaneous
speed at a particular time t=a
- Derivative at a point